This graduate textbook covers the basic formalism of supergravity, as well as its modern applications, suitable for a focused first course. Assuming a working knowledge of quantum field theory, Part I gives the basic formalism, including on- and off-shell supergravity, the covariant formulation, superspace and coset formulations, coupling to matter, higher dimensions and extended supersymmetry. A wide range of modern applications are introduced in Part II, including string theoretical (T- and U-duality, AdS/CFT, susy and sugra on the worldsheet, superembeddings), gravitational (p-brane solutions and their susy, attractor mechanism, Witten's positive energy theorem) and phenomenological (inflation in supergravity, supergravity no-go theorems, string theory constructions at low energies, minimal supergravity and its susy-breaking). The broader emphasis on applications than competing texts gives Ph.D. students the tools they need to do research that uses supergravity and benefits researchers already working in areas related to supergravity.
1. Introduction to general relativity 1: kinematics and Einstein equations; 2. Introduction to general relativity 2: Vielbein and spin connection, anti-de Sitter space, black holes; 3. Introduction to supersymmetry 1: Wess–Zumino models, onshell and off-shell supersymmetry; 4. Introduction to supersymmetry 2: multiplets and extended supersymmetry; 5. Introduction to supersymmetry 3: superspace formalism in d = 4. Perturbative susy breaking; 6. 4-dimensional on-shell supergravity and how to count degrees of freedom; 7. 3-dimensional N = 1 off-shell supergravity; 8. Coset theory and rigid superspace; 9. Covariant formulation of YM in rigid superspace and local superspace formalisms; 10. N = 1 4-dimensional off-shell supergravity; 11. N = 1 4-dimensional supergravity in superspace; 12. Superspace actions and coupling supergravity with matter; 13. Kaluza–Klein (KK) dimensional reduction and examples; 14. Spherical harmonics and the KK expansion on sphere, coset and group spaces; 15. N = 2 sugra in 4 dimensions, general sugra theories and N = 1 sugra in 11 dimensions; 16. AdS4 × S7 nonlinear KK compactification of 11-dimensional supergravity and related notions; 17. (Abelian and non-Abelian) T-dualities and other solution-generating techniques: TsT, O(d, d), null Melvin twist; 18. Extremal and black p-brane solutions of supergravity, Tseytlin's harmonic function rule; 19. Supersymmetry of solutions, classification via susy algebra, intersecting brane solutions; 20. U-duality group acting on supergravity theories and on solutions, M-theory unification; 21. Gravity duals: decoupling limit and Penrose limits on solutions and algebras; 22. Supersymmetric AdS/CFT gravity dual pairs and their deformations (susy, marginal, integrable); 23. Extremal black holes, the attractor mechanism, and holography; 24. Supersymmetric string (NS-R, GS, Berkovits) and supergravity on the worldsheet vs. spacetime supergravity; 25. Kappa symmetry and spacetime supergravity equations of motion, superembedding formalism; 26. Supergravity and cosmological inflation models; 27. Maldacena–Núñez and supergravity no-go theorems, loopholes; 28. Witten's positive energy theorem in general relativity and connection with supergravity; 29. Compactification of low energy string theory; 30. Towards realistic embeddings of the Standard Model using supergravity; 31. Minimal sugra, phenomenology and models of susy breaking; References; Index.
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